Biophysical theory regards the electrophysiological interaction between passive and active patches of nerve membrane as functionally significant. Important examples are interactions such as an active soma attached to a dendritic tree, myelinated nerves, and the possibility of denritic spines with excitable spine head membranes. The aim of this project is to explore, using mathematical modeling, analysis, and numerical computation the functional implications of these interactions. We expand this study to include a new class of excitability problems involving a slowly-varying control parameter and we also continue to study the voltage response of nerve membrane when subjected to periodic forcing.